March 09, 2006 5:30 am
Larson ch 1.3, p. 64 - 66
39.

y = (x^3 + 8)/(x + 2)

Limit[y, x -> -2]

Plot[y, {x, -5, 5}, PlotStyle -> Red];

40.

Clear[y]

y = (x^3 + 1)/(x + 1)

Limit[y, x -> -1]

Plot[y, {x, -5,  5},  PlotStyle -> Blue];

41.

Clear[y]

y = (x - 5)/(x^2 - 25)

Limit[y, x -> 5]

Plot[y, {x, -5, 5}, PlotStyle  -> Red];

42.

Clear[y]

y = (2 - x)/(x^2 - 4)

Limit[y, x -> 2]

Plot[y, {x, -5, 2}, PlotStyle -> Blue];

43.

Clear[y]

y = (x^2 + x - 2)/(x^2 - 1)

Limit[y, x -> 1]

Plot[y, {x, -5, 1},  PlotStyle -> Blue];

44.

Clear[y]

y = ((Sqrt[2 + x]) - Sqrt[2])/x

Limit[y, x -> 0]

57.

Clear[y]

y = Sin[x]/(5  x)

Limit[y, x -> 0]

Plot[y, {x, -2 π, 2  π}, 
        PlotStyle -> Red];

58.

Clear[y]

y = (3 (1 - Cos[x]))/x

Limit[y, x -> 0]

Plot[y, {x, -2 π, 2  π}, 
        PlotStyle -> Blue];

59.

Clear[y]

y = (Sec[θ] - 1)/(θ Sec[θ])

Limit[y, θ -> 0]

Plot[y, {θ, -2 π, 2  π}, 
        PlotStyle -> Red];

60.

Clear[y]

y = Cos[θ] Tan[θ]/θ

Limit[y, θ -> 0]

Plot[y, {θ, -2 π, 2  π}, 
        PlotStyle -> Blue];

61.

Clear[y]

y = (Sin[x]^2)/x

Limit[y, x -> 0]

Plot[y, {x, -2 π, 2  π}, 
        PlotStyle -> Red];

62.

Clear[y]

y = ((Tan[x])^2)/x

Limit[y, x -> 0]

Plot[y, {x, -2 π, 2  π}, 
        PlotStyle -> Blue];